Thermomagnetic properties of the strongly correlated semimetal - PowerPoint PPT Presentation

MAX-PLANCK-INSTITUT FÜR CHEMISCHE PHYSIK FESTER STOFFE Thermomagnetic properties of the strongly correlated semimetal CeNiSn Niels Oeschler Max Planck Institute for Chemical Physics of Solids, Dresden, Germany

MAX-PLANCK-INSTITUT FÜR CHEMISCHE PHYSIK FESTER STOFFE Acknowledgements: Measurements: U. Köhler, MPI CPfS, Dresden, Germany P. Sun, MPI CPfS, Dresden, Germany S. Paschen, Vienna University of Technology, Austria F. Steglich, MPI CPfS, Dresden, Germany Samples: T. Takabatake, Hiroshima University, Japan

Outline Introduction Thermoel. and thermomagn. effects Exp. setup Correlated semimetal CeNiSn Results Resistivity and Hall effect Thermopower Nernst effect and Righi-Leduc effect Discussion Field-dependent thermopower Nernst effect Summary

Introduction Thermoel. and thermomagn. Effects z y Charge transport: J = σ E - σ S Δ T B Heat transport: J Q = σ STE - κΔ T heater x Thermal conductivity: κ = J Q / Δ T x J Q Δ T x U x Thermopower: S = -U x / Δ T x bath

Introduction Thermoel. and thermomagn. Effects z y Charge transport: J = σ E - σ S Δ T B Heat transport: J Q = σ STE - κΔ T heater x Thermal conductivity: κ = J Q / Δ T x J Q Thermopower: S = -U x / Δ T x Nernst effect: ν = -U y / Δ T x B bath Righi-Leduc effect: L = - κ y /B Δ T y / Δ T x U y Δ T y

Introduction Thermomagn. Effects: Ettingshausen cooling L c source/hot B Δ T B j j L h sink/cold Thermomagn. figure of merit Z mag T infinite stage Ettingshausen device α ⎛ − ⎞ σ υ 2 2 ( ) L Z T B T ⎜ ⎟ Δ = = c 1 Δ = mag cold T T ⎜ ⎟ Z T T max hot mag κ ⎝ ⎠ max L 2 h

Kondo Insulator E E (a) (b) (c) (d) unperturbed conduction band unperturbed 4 f band E F E F hybridized bands 0 2 π /a 0 2 π /a k N ( E ) k N ( E ) Heavy fermion metals Kondo insulator • ρ ~ -ln T at T ≈ T K • ρ ~ -ln T at T ≈ T K • enhanced DOS at E F below ~ T K • gap below ~ T g � metal-like behavior at low T � insulating behavior at low T

Introduction Experimental Setup: 4 He cryostat horizontal 7T magnet optimized for small samples with low κ Δ T: chromel-AuFe thermocouples U: copper wires, nanovoltmeter

CeNiSn Ce samples Ni orthorhombic crystal structure Sn chains of Cerium ions along a c easy a axis Czochralski method annealed by SSE a b energy scales crystal field levels: k B Δ CEF ≈ 230K, 460K Kondo temp.: T K ≈ 56 K pseudogap Δ / k B ≈ 10 K below T ≈ 10 K c no ordering down to 25 mK b a

CeNiSn gap structure pseudogap opens around 10K d I /d V residual states at E F metallic ρ , large Sommerfeld coeff. V (mV) T. Ekino et al., Phys. Rev. Lett. 75 , 4262 (1995) gap suppression • magnetic fields ~10 T // a • pressure ~ 2 GPa • substitution (Ce/La and Ni/Cu,Co) ~ 10 % K. Izawa et al., J. Phys. Soc. Jpn. 65 , 3119 (1996)

CeNiSn - Kondo Insulator? sensitive dependence on sample purity ( ρ , MR , R H ) residual DOS near E F (NMR, c P , ρ , κ ) ⇒ CeNiSn – Kondo semimetal K. Izawa et al., J. Phys. Soc. Jpn. 65 , 3119 (1996) H. Ikeda and K. Miyake, J. Phys. Soc. Jpn. 65 , 1769 (1996) G. Nakamoto et al., J. Phys. Soc. Jpn. 64 (12), 4834 (1995)

Experimental Single crystals (#5) - Czochralski + SSE - best available samples - Orientation: Laue, χ , ρ ( a / c ) - ca. 4 x 4 x 0.8 mm³ G. Nakamoto et al., J. Phys. Soc. Jpn. 64 (12), 4834 (1995) - Measurements: q // b ; B // a , c 200 CeNiSn No.3 Measurements: j // b, B // a 150 ρ ( μΩ cm) • Thermal conductivity 0 T 100 1 T • Thermopower at +B and –B 2 T 50 4 T • Nernst effect 7 T 0 1.5 5 10 50 • Thermal Hall effect T (K)

Results: Thermopower CeNiSn #4 CeNiSn #5 40 B = 0 T q //b 20 S (µV/K) 0 -20 G. Nakamoto et al., Physica B 306 & 307 , 840 (1995) sample No 1 sample No 3 CeNiSn type unknown -40 1.5 5 10 50 100 T (K) 60 S (µV/K) 40 • Kondo system with CEF splitting 20 • largest negative S ever observed b-axis 0 • very precise orientation ! 0 10 20 30 40 T (K) J. Sakurai et al., Physica B 306 & 307 , 834 (1995)

Field-dep. Thermopower 40 literature: CeNiSn #5, No. 3 • strong sample q //b, B //a 20 dependence at low T • no comparable results 0 S (µV/K) in field 0 T -20 1 T 2 T 4 T -40 7 T 1.5 2 3 4 5 6 7 89 10 20 30 40 T (K) B // a: - enhanced values of | S | - shift of the minimum to lower T B // c: - similar, but less pronounced

Nernst effect q // b, B // a B // c 0 0 1 T 5.5 T 4 T 0.5 T -20 -20 7 T 2 T 1 T 7 T 3 T 2 T -40 -40 0 0 N (µV/K) N (µV/K) -60 -60 -5 -5 ν (µV/KT) ν (µV/KT) -10 -80 -80 -10 -15 -100 -100 -15 -20 2 4 6 8 10 2 4 6 8 10 T (K) -120 -120 T (K) 1.5 5 10 50 1.5 5 10 50 T (K) T (K) large values of N below 10 K (opening of the gap) • scaling for B // a (easy axis!) • shift of minimum for B // c

Discussion: Thermopower variation due to 10 - sample dependence 0 -10 - misorientation U long / Δ T -20 - non-negligible Nernst contribution -30 + 2 T - 2 T -40 0 2 4 6 8 10 T (K)

Discussion: Thermopower variation due to 10 - sample dependence 0 -10 - misorientation U long / Δ T -20 - non-negligible Nernst contribution -30 + 2 T - 2 T -40 0 2 4 6 8 10 T (K) 0 -10 U long / Δ T -20 -30 N (2T) ( U + - U - )/(2 Δ T ) -40 N (2T) (U + -U - )/2 Δ T 0 2 4 6 8 10 T (K)

Discussion: Thermopower variation due to 10 - sample dependence 0 -10 - misorientation U long / Δ T -20 - non-negligible Nernst contribution -30 + 2 T - 2 T -40 0 2 4 6 8 10 T (K) 0 -10 U long / Δ T -20 7 deg -30 N (2T) ( U + - U - )/(2 Δ T ) -40 N (2T) (U + -U - )/2 Δ T 0 2 4 6 8 10 T (K)

Discussion: Thermopower variation due to 10 - sample dependence 0 -10 - misorientation U long / Δ T -20 - non-negligible Nernst contribution -30 + 2 T - 2 T -40 0 2 4 6 8 10 T (K) � first systematic study of 0 S ( T , B ) including: -10 • best available samples U long / Δ T -20 7 deg • precise orientation -30 N (2T) ( U + - U - )/(2 Δ T ) • correction for the Nernst signal -40 N (2T) (U + -U - )/2 Δ T 0 2 4 6 8 10 T (K)

Field-dep. Thermopower 40 literature: CeNiSn #5, No. 3 • strong sample q //b, B //a 20 dependence at low T • no comparable results 0 S (µV/K) in field 0 T -20 1 T 2 T 4 T -40 7 T 1.5 2 3 4 5 6 7 89 10 20 30 40 T (K) B // a: - enhanced values of | S | - shift of the minimum to lower T B // c: - similar, but less pronounced

Discussion: Thermopower position of the minimum 3.5 3.0 T min (K) 2.5 2.0 B // a B // c 1.5 0 2 4 6 8 B (T) - effect larger for B // a

Discussion: Thermopower position of the minimum 3.5 3.0 T min (K) 2.5 2.0 B // a B // c 1.5 0 2 4 6 8 B (T) - effect larger for B // a - extrapolation // a: B c = 14 T (MR: 18 T) � shift ~ closing of the gap

Discussion: Thermopower position of the minimum 18 3.5 16 3.0 14 Δ E (meV) T min (K) 2.5 12 Δ E 2.0 10 B // a B // c 8 1.5 0 2 4 6 8 B (T) - effect larger for B // a - extrapolation // a: B c = 14 T (MR: 18 T) � shift ~ closing of the gap ( Δ E from tunneling spectroscopy) T. Ekino et al., Physica B 230-232 , 635 (1997)

Discussion: Thermopower position of the minimum value at the minimum -25 18 3.5 -30 16 3.0 -35 14 S min (µV/K) Δ E (meV) T min (K) -40 2.5 12 Δ E -45 B // a 2.0 10 B // a B // c B // c -50 8 1.5 0 2 4 6 8 0 2 4 6 8 B (T) B (T) - effect larger for B // a - effect larger for B // a - extrapolation // a: B c = 14 T - change of the DOS near E F due to Zeeman splitting ( c P ) (MR: 18 T) � shift ~ closing of the gap - similar results for S ( T ) at low T ( Δ E from tunneling spectroscopy) K. Izawa et al., J. Phys. Soc. Jpn. 65 , 3119 (1996) T. Ekino et al., Physica B 230-232 , 635 (1997) S. Paschen et al., Phys. Rev. B 62 , 14912 (2000)

Discussion: Thermopower V-shaped DOS in field increasing B ∂ ln N ∝ S ∂ ε similar analysis for C P ( T,B ) E F (enhanced γ value in field) K. Izawa et al., J. Phys. Soc. Jpn. 65 , 3119 (1996)

Results: Nernst effect q // b, B // a B // c 0 0 1 T 5.5 T 4 T 0.5 T -20 -20 7 T 2 T 1 T 7 T 3 T 2 T -40 -40 0 0 N (µV/K) N (µV/K) -60 -60 -5 -5 ν (µV/KT) ν (µV/KT) -10 -80 -80 -10 -15 -100 -100 -15 -20 2 4 6 8 10 2 4 6 8 10 T (K) -120 -120 T (K) 1.5 5 10 50 1.5 5 10 50 T (K) T (K) large values of N below 10 K (opening of the gap) • scaling for B // a (easy axis!) • shift of minimum for B // c → open question: weak sensitivity to magnetic fields // a

Discussion: Nernst effect Boltzmann approximation: Nernst effect: π ∂ τ 2 2 ν a = ν n - ε yy / κ yy L xy k T = ν n n B N ∂ ε 3 * m ν n : normal Nernst coeff. E F ν a : adiabatic Nernst coeff. σ Θ H = yx with Hall angle tan due to transverse temp. gradient σ xx ≈ π Θ 2 2 tan For CeNiSn, Δ T y ≈ 0, L xy ≈ 0 k T n ν n B H N 3 Be E (below resolution limit) F → ν a = ν n Large Nernst coefficient: • Low charge carrier concentration • Small Fermi energy

Discussion: Nernst effect How to obtain large Nernst coefficients? N Behnia et al., Phys. Rev. Lett. 98 , 076603 (2007)

Discussion: Nernst effect How to obtain large Nernst coefficients? Bi normal semimetal N Behnia et al., Phys. Rev. Lett. 98 , 076603 (2007)